Neuroblastoma, which arises from the sympathetic nervous system, is the most common extracranial solid tumor of childhood. One of the challenges faced in the treatment of neuroblastoma is that while many children with metastatic disease initially respond to therapy, the tumor recurs and the child dies from progressive disease. The causes for treatment failure are mutifactorial, but acquired drug resistance probably plays a major role. This study will evaluate the pharmacokinetics and clinical toxicities of the combination of buthionin sulfoximine (BS0) and melphalan in pediatric patients with neuroblastoma. Pre-clinical studies have shown that glutathione plays a role in chemotherapy resistance by detoxification of alkylator damage and that BSO, a selectidve inhibitor of glutathione synethesis, can restore sensitivity of alkylating agents. An additional goal of this study is to document glutathione (GSH) depletion in peripheral blood lymphocytes, normal marrow and neuroblastoma cells found in the bone marrow.